Publications [#323246] of Jian-Guo Liu

Papers Published

1. Liu, JG; Xu, X, Existence theorems for a multidimensional crystal surface model, SIAM Journal on Mathematical Analysis, vol. 48 no. 6 (January, 2016), pp. 3667-3687, Society for Industrial & Applied Mathematics (SIAM) [doi]
   (last updated on 2025/02/21)

   Abstract:
   In this paper we study the existence assertion of the initial boundary value problem for the equation @u/@t = Δe-Δu. This problem arises in the mathematical description of the evolution of crystal surfaces. Our investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue decomposition theorem, and the exponential nonlinearity somehow "cancels" it out. The net result is that we obtain a solution u that satisfies the equation and the initial boundary conditions in the almost everywhere (a.e.) sense.